Noise-induced enhancement of regime lifetimes -- A data-driven approach using deterministic trajectories

TL;DR

This paper explores how small noise can unexpectedly prolong the lifetime of dynamical regimes in atmospheric models, introducing a data-driven method to detect this phenomenon called stochastic inertia.

Contribution

It presents a novel numerical technique using Markov chains on deterministic trajectories to identify stochastic inertia in complex dynamical systems.

Findings

Small noise can increase regime lifetimes, demonstrating stochastic inertia.

The proposed method accurately predicts stochastic inertia in simple models.

Application to atmospheric models confirms the phenomenon's relevance.

Abstract

We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state space faster. However, for relevant systems with complexities ranging from phenomenological toy models to reduced models of atmospheric dynamics, this intuition has proven misleading. As long as the noise is sufficiently small, the noisy system stays in regimes of interest on average longer than its deterministic counterpart, an effect we call ``stochastic inertia''. This phenomenon has been observed through extensive numerical simulations for different noise levels. We propose a numerical technique for testing the occurrence of stochastic inertia, constructing, for any fixed noise level, a Markov chain on the set of points given by a sufficiently long trajectory of the system without noise. The method is shown to correctly predict the presence of stochastic inertia in simple systems, and its utility is demonstrated on a paradigm model of atmospheric dynamics.